You can use tea bags in a teapot. Of course tea purists will argue that tea bags are inferior to loose tea, as they are only the leftover dust and scraps of the higher quality tea leaves.
First, always, always start with cold water. It retains more oxygen and gives a fuller, rounder flavor. Do not use hard tap water, instead try bottled or filtered water. Also, do not fill up your teakettle the night before, always use fresh water.
While your water is heating on the stove, warm your teapot by filling it up with very hot tap water. Leave the water in there until your other water is ready. Then drain the teapot completely and fill it with the water from the stove.
Lightly dunk the tea bags (I use two tea bags per teapot for brewing) into the teapot. A big faux pas when making tea, besides the incorrect temperature of the water; tea bags are dunked and then squeezed out the tea bag. Squeezing out the bag makes the tea bitter. Wring out the tea bag into cup. Then adding copious amounts of sugar to the tea to overcome what I’m sure was a bitter taste. Don’t do that. Do not touch the tea bag once it’s in the cup or teapot, until it is time to remove it.
For black tea, you want to bring the water to a full boil but remove the teakettle off the heat as soon as the water begins to boil. Continuing to boil the water boils all the oxygen out and the tea actually has a flatter flavor. Brew the tea for 4-5 minutes.
When it comes to green tea, white tea or herbal teas, which are more delicate, you want to remove the teakettle from the heat right before the water comes to a boil, about 170 degrees F. Brew the tea no more than 3 minutes.
Overbrewed tea will also taste bitter. Do not leave the bag in contact with the water longer than necessary.